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The paradox of group behaviors based on Parrondo’s games


  • Xie, Neng-gang
  • Guo, Jia-yi
  • Ye, Ye
  • Wang, Chao
  • Wang, Lu


We assume a multi-agent model based on Parrondo’s games. The model consists of game A between individuals and game B. In game A, two behavioral patterns are defined: competition and inaction. A controlled alternation strategy of behavioral pattern that gives a single player the highest return is proposed when game A+B is played randomly. Interesting phenomena can be found in collective games where a large number of individuals choose the behavioral pattern by voting. When game B is the capital-dependent version, the outcome can be better for the players to vote randomly than to vote according to their own capital. An explanation of such counter-intuitive phenomena is given by noting that selfish voting prevents the competition behavior of game A that is essential for the total capital to grow. However, if game B is the history-dependent version, this counter-intuitive phenomenon will not happen. The reason is selfish voting results in the competition behavior of game A, and finally it produces the winning results.

Suggested Citation

  • Xie, Neng-gang & Guo, Jia-yi & Ye, Ye & Wang, Chao & Wang, Lu, 2012. "The paradox of group behaviors based on Parrondo’s games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6146-6155.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:6146-6155
    DOI: 10.1016/j.physa.2012.07.024

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    References listed on IDEAS

    1. Dinís, Luis & Parrondo, Juan M.R., 2004. "Inefficiency of voting in Parrondo games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 701-711.
    2. Mihailović, Zoran & Rajković, Milan, 2006. "Cooperative Parrondo's games on a two-dimensional lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 244-251.
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